That is an interesting, and I believe wrong, assessment. Some customers demand the ability to pay with plastic. And, while it would be nice to be able to tell them that you don't because you are passionate - passion don't pay the rent.
When I had my gallery - heck even now - my credit card facilities consisted of one of those old mechanical CC imprint machines.
In these type of instances, many galleries I deal with do direct electronic bank transfer in house rather than CC. It's also much secure than CC.
If I purchase a piece of art/furniture for over 1000, I do a direct bank transfer at the gallery. That way the owner doesn't pay CC fees and they get immediate confirmation of transfer. Sure, it may take 5 mins, but in a "gallery" setting that's not a big deal. Usually, that's when the sekt (small) or champagne (large purchases) comes out anyway, after a friendly negotiation.
I can't imagine many places, except retail chains, that have customers demanding CC options.